Lie Rings and Lie Algebras with Ideal Spreads are Abelian or of Rank 2

A Lie ring or Lie algebra L possessing an ideal spread (that is a spread of subrings or subalgebras which is stable under Lie multiplication) is either Abelian or there is a field K' that operates on L so that L can be seen as K'-Lie algebra of rank 2. If L was a K-Lie algebra then L' is a field extension of K. The given spread is just the set of all one-dimensional K'-subspaces of L.